TABLE 5 Age-Specific Birth Rates for Girl Children, Ages 15 to 45, Taiwan, 1964 and 1966 Change 1964 1966 &F 15-19 0.018 0.019 +0.001 20-24 0.123 0.133 +0.010 25-29 0.162 0.159 -0.003 30-34 0.104 0.092 -0.012 35-39 0.058 0.044 -0.014 40-44 0.025 0.018 -0.007 Total 0.490 0.465 -0.025 Total X 5 = GRR 2.45 2.32 -0.13 Intrinsic rate lOOOr 29.29 28.48 -0.81 Source: Author's calculations. tionately less than this because the generation tended to become shorter over the 2 years, and mortality somewhat improved. In fact, the intrinsic rate r of Taiwan fell from 0.02929 to 0.02848 in the 2-year period, only 52 percent of the proportional drop in the GRR. The change in age-specific rates of Table 5, weighted by the last column of Table 4, provides the net impact on r of fertility change, the remainder being due to improvement in mortality. The 2-year interval is of little interest by itself; what we really care about is the indication for the future. Suppose that we extend the GRR forward; the drop of 2.45 to 2.32 in 2 years suggests a drop of 0.06 per year, and linear extrapolation suggests that in a further 20 years the population would be just reproducing itself. This agrees with the 1956 to 1964 trend, which showed a slightly greater rate of annual descent of the Gross Reproduction Rate. But aside from the above proof that, from the viewpoint of controlling r, a fall at the oldest age is worth half or less what a fall at the younger ages is worth, another and much grosser point enters: that the age-specific rate at any age cannot go below zero. This requires no theory for its elaboration. We have implicitly offended against it in projecting the 1964 to 1966 trend of the GRR. On the straight line the birth rate to those over 40 will reach zero within another 5 or so years, and to those over 30 will reach zero in about 10 years. Before that time the overall decline will taper off unless the women below 30 reduce their rates. Quite different long-term projections would be obtained from projecting linearly age by age, taking account of the floor at zero, from those obtained by projecting the total.an would marry older and have her children later within marriage; her length of generation— a measure something like the average age of childbearing-was 27.3 years against the United States 26.2 years. This means a more rapid turnover of generations in the United States.